Boolean or cuts without creating ngons
Cut your hole >  in Edit Mode select the loop of faces inside the new hole > Ctrl+Numpad + to grow the selection once or twice > Ctrl+T for "triangulate faces" (or you can right click and it should be in the pop up menu; or go to the menu for 'faces') > Alt+J for "turn triangles into quads" (this is in the 'faces' menu too).

Not sure how well this will work for your needs, but it's quick.  GL OP